The course is an introduction to Time Series Analysis and Forecasting. The level is the first-year graduate in Mathematics with a prerequisite knowledge of basic inferential statistical methods. The aim of the course is to present important concepts of time series analysis (Stationarity of stochastic processes, ARIMA models, forecasting etc.). At the end of the course, the student should be able to select an appropriate ARIMA model for a given time series.
Stochastic processes (some basic concepts). Stationary stochastic processes. Autocovariance and autocorrelation functions. Ergodicity of a stationary stochastic process. Estimation of moment functions of a stationary process. ARIMA models. Estimation of ARIMA models. Building ARIMA models. Forecasting from ARIMA models
Time Series Analysis Univariate and Multivariate Methods, 2nd Edition, W. W. Wei, 2006, Addison Wesley.
Time Series Analysis, J. Hamilton, 1994, Princeton University Press.
Time Series Analysis and Its Applications with R Examples, Shumway, R. and Stoffer, D., 2006, Springer.
Introduction to Time Series and Forecasting. Second Edition, P. Brockwell and R. Davis, 2002, Springer.